U.S. patent application number 11/756337 was filed with the patent office on 2009-07-30 for method, system, and apparatus for statistical evaluation of antihypertensive treatment.
Invention is credited to Pedro Mateo Riobo Aboy.
Application Number | 20090192392 11/756337 |
Document ID | / |
Family ID | 40899934 |
Filed Date | 2009-07-30 |
United States Patent
Application |
20090192392 |
Kind Code |
A1 |
Riobo Aboy; Pedro Mateo |
July 30, 2009 |
Method, system, and apparatus for statistical evaluation of
antihypertensive treatment
Abstract
A novel method, system, and apparatus--the RDH Method--for
evaluating antihypertensive treatment efficacy across patient
populations is disclosed. In accordance to one embodiment, the RDH
is a population vector index and graphical method that provides the
means for the statistical assessment of antihypertensive treatment
reduction, duration, and homogeneity using ambulatory blood
pressure monitoring (ABPM). The population RDH was specifically
designed as a tool to evaluate and compare blood pressure (BP)
coverage offered by antihypertensive drugs over 24 h in
populations. In accordance to one embodiment, the population RDH is
a three-component vector index that incorporates information about
the reduction, duration, and homogeneity of antihypertensive
treatment, as well as their statistical significance over the 24 h
period. In the preferred embodiment, the population RDH components
quantify: 1) the total number of statistical significant BP
reductions, 2) the maximum number of consecutive statistical
significant reductions, and 3) the maximum number of consecutive
non-significant reductions over the 24 hours, respectively; and
reports two population graphs that characterize the effect of the
treatment. The output of the RDH index can be used in clinical
trials to characterize the effects of antihypertensive medications,
and in clinical practice to guide antihypertensive treatment.
Inventors: |
Riobo Aboy; Pedro Mateo;
(Portland, OR) |
Correspondence
Address: |
ABOY&ASSOCIATES PC | Dr. Mateo Aboy #64040;www.aboypatentlaw.com
522 SW 5th Ave, Suite 1265
Portland
OR
97204
US
|
Family ID: |
40899934 |
Appl. No.: |
11/756337 |
Filed: |
May 31, 2007 |
Current U.S.
Class: |
600/485 |
Current CPC
Class: |
A61B 5/4833 20130101;
A61B 5/021 20130101 |
Class at
Publication: |
600/485 |
International
Class: |
A61B 5/02 20060101
A61B005/02 |
Claims
1. A method for evaluating antihypertensive treatment and guiding
antihypertensive therapy using parametric statistical inference,
comprising: (a) obtaining and analyzing two synchronized ABPM
recordings: pre-treatment and post-treatment (b) calculating the
mean of each category k for each subject j before and after the
treatment x _ k j = i = 1 L k , j x k , i j L k , j y _ k j = i = 1
L k , j ' y k , i j L k , j ' ( 14 ) ##EQU00010## (c) creating
population composites of category k, before x.sub.k and after
treatment y.sub.k, x.sub.k=( x.sub.k.sup.1, x.sub.k.sup.2, . . . ,
x.sub.k.sup.j,, x.sub.k.sup.J) (15) y.sub.k=( y.sub.k.sup.1,
y.sub.k.sup.2, . . . , y.sub.k.sup.j,, y.sub.k.sup.J) (16) (d)
creating a vector containing the BP differences,
d.sub.k=x.sub.k-y.sub.k=( x.sub.k.sup.1- y.sub.k.sup.1,
x.sub.k.sup.2- y.sub.k.sup.2, . . . , x.sub.k.sup.J-
y.sub.k.sup.J)=(d.sub.1,d.sub.2, . . . ,d.sub.J) (17) (e)
performing a paired-sample t test to test if the mean BP reduction
in category k is greater than zero, t k = d _ k se ^ d _ k = j = 1
J x _ k j - y _ k j J s d k 2 J s d k 2 = j = 1 J ( d j - d _ ) 2 J
- 1 ( 18 ) ##EQU00011## for each category k, k=1, . . . , 24,
assessing the statistical significance of of the mean BP reduction
by dividing the mean BP difference d.sub.k for category k over its
standard error s .sub. d.sub.k. (f) defining the parametric
embodiment of the population RDH vector as RDH=(c.sub.1, c.sub.2,
c.sub.3) where c.sub.1=Total number of statistically significant
reductions c.sub.2=Maximum number of consecutive statistically
significant reductions c.sub.3=Maximum number of consecutive
statistically non-significant reductions
2. A method for evaluating antihypertensive treatment and guiding
antihypertensive therapy using nonparametric statistical inference,
comprising: (a) creating a vector containing the BP differences,
d.sub.k=x.sub.k-y.sub.k=( x.sub.k.sup.1- y.sub.k.sup.1,
x.sub.k.sup.2- y.sub.k.sup.2, . . . , x.sub.k.sup.J- y.sub.k.sup.J)
(19) (b) calculating the statistic of interest from d.sub.k,
{circumflex over (.theta.)}.sub.k=s(d.sub.k), which in this case is
the mean BP reduction d, .theta. ^ k = s ( d k ) = j = 1 J d k , j
J ( 20 ) ##EQU00012## (c) analyzing the empirical distribution
{circumflex over (T)}.sub.k to obtain bootstrap samples
d.sub.k*=(d.sub.k,1*,d.sub.k,2*, . . . , d.sub.k,J*) by random
sampling of {circumflex over (T)}.sub.k {circumflex over
(T)}.sub.k.fwdarw.d.sub.k*=(d.sub.km1*,d.sub.k,2*, . . .
,d.sub.k,J*) and calculating bootstrap replications of the
statistic of interest {circumflex over (.theta.)}.sub.k=s(d.sub.k*)
to estimate the probability distribution {circumflex over
(.theta.)}.sub.k*, (d) analyzing the histogram of {circumflex over
(.theta.)}.sub.k*(b), b=1,2, . . . , B as an estimate of the
probability density function of the mean BP differences for
category k across the population; the bootstrap confidence
intervals for the population BP reduction in class k are obtained
as {circumflex over (.theta.)}.sub.k.sub.lo=100.alpha..sup.th
percentile of {circumflex over (.theta.)}.sub.k*'s distribution
{circumflex over (.theta.)}.sub.k.sub.lo=100(1-.alpha.).sup.th
percentile of {circumflex over (.theta.)}.sub.k*'s distribution
(21) and concluding that if this interval contains zero, it cannot
be assumed with (1-2.alpha.) confidence that the parameters of the
two populations are statistically different, (e) defining the
nonparametric population RDH vector as RDH=(c.sub.1, c.sub.2,
c.sub.3) analogous to the parametric case.
3. The method of claim 1, further comprising generating a results
image illustrating the antihypertensive treatment effects,
including a user-specified confidence interval of the reduction in
hypertension on the patient population across the 24-hours.
4. The method of claim 1, further comprising generating a results
image the antihypertensive treatment effects for each individual in
the same plot, including the statistical significance of the
reduction and the proportion of subjects where the treatment
results in statistical significant reduction across the
24-hours.
5. The method of claim 2, further comprising generating a graph
illustrating the antihypertensive treatment effects, including a
user specified confidence interval of the reduction in hypertension
on the patient population across the 24-hours.
6. The method of claim 2, further comprising generating a results
image illustrating the antihypertensive treatment effects for each
individual in the same plot, including the statistical significance
of the reduction and the proportion of subjects where the treatment
results in statistical significant reduction across the
24-hours.
7. A method for evaluating antihypertensive treatment reduction,
duration, homogeneity, efficacy, effectiveness comprising the
evaluation of hour-by-hour (overlapping and nonoverLapping)
pre-treatment and post-treatment ABPM recordings using parametric
or nonparametric statistical inference techniques to determine
whether the blood pressure reduction was due to chance or to the
treatment working as intended.
8. The method of claim 7, further comprising analyzing ABPM
recording corresponding to different antihypertensive treatments to
determine chronopharmacodynamical bioequivaLence between
treatments.
9. The method of claim 1 or claim 2, wherein the threshold used for
establishing statistical significance is user-specified to enable
efficacy characterization.
10. A machine or system, comprising hardware and software that
implements the methods of claim 1.
11. A machine or system, comprising hardware and software that
implements the methods of claim 2.
12. A machine or system, comprising hardware and software that
implements the methods of claim 3.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] Not Applicable
FEDERALLY SPONSORED RESEARCH
[0002] Not Applicable
SEQUENCE LISTING OR PROGRAM
[0003] Not Applicable
BACKGROUND
[0004] 1. Field of Invention
[0005] This invention relates to evaluation of antihypertensive
treatments, specifically it relates to methods, system or apparatus
for statistical evaluation of antihypertensive treatment reduction,
duration, homogeneity, and efficacy.
[0006] 2. Prior Art
[0007] Hypertension is a serious chronic disorder that affects over
1 billion people worldwide. In the United States alone,
hypertension affects over 55 million Americans. Chronic
hypertension is associated with increased morbidity and mortality.
When left untreated, the prolonged elevation of BP produces serious
end organ damage, including myocardial infarction, heart failure,
angina pectoris, left ventricular hypertrophy, prior coronary
revasculazation, kidney disease, stroke, peripheral arterial
disease, transient ischemic attack, and retinopathy [1,2].
[0008] The ultimate objective in treating hypertension is to reduce
cardiovascular and renal morbidity and mortality. A secondary goal
is to accomplish BP control without decreasing the quality of life
with the drugs employed. The incidence of mortality and morbidity
decreases significantly when hypertension is diagnosed early and
property treated with adequate antihypertensive treatments. Drug
therapy can reduce both BP and the risk of long-term complications.
However, since antihypertensive treatment is not curative it is
necessary to continue treatment indefinitely. This presents one of
the first challenges in the treatment of hypertension. Despite the
potential serious harm of elevated BP, hypertension is usually
asymptomatic until after end-organ damage. Thus, since elevated BP
often doesn't cause discomfort, many people with essential
hypertension do not get treated. Even when hypertension is property
diagnosed, compliance to treatment is a significant problem. As a
consequence, single dose antihypertensive drugs with 24-h duration
of action are preferred to treat essential hypertension.
Single-dose treatments help promote compliance. However, it is
important that single-dose drugs intended for monotherapy regimes
have an effective 24-h duration of action. Single-dose treatments
must provide adequate BP control for 24-h to be useful as
antihypertensive drugs.
[0009] The introduction of ambulatory blood pressure monitoring
(ABPM) has enabled clinicians and researchers to provide better
diagnosis and treatment of hypertension. ABPM has drastically
improved the ability to assess the efficacy of antihypertensive
treatment in clinical studies and in medical practice [3-5]. ABPM
offers significant advantages over clinic sphygmomanometric
readings as a toot to property diagnose, treat hypertension, and
evaluate antihypertensive treatment. These include: 1) ABPM is
characterized by higher reproducibility, 2) it is not subject to
observer bias and white-coat effect, 3) it enables practitioners to
test the effectiveness of a given antihypertensive drug in daily
life conditions, and 4) can be used to estimate the
pharmacodynamics of antihypertensive drugs [6-8]. ABPM enables
clinicians and researchers to obtain accurate and reproducible data
on the circadian pattern of BP. With ABPM, multiple automatic
measurements of BP are obtained at specific intervals throughout
the day. However, despite all the advantages of ABPM over casual BP
readings, the analytic techniques and indices used to analyze the
ABPM recordings are not taking full advantage of the ABPM benefits
and the current indices used to evaluate antihypertensive
drugs--the trough:peak ratio (TP) and the smoothness index
(SI)--have significant limitations and do not provide a complete
and accurate characterization of the treatment [7,9-14].
[0010] Despite its significant benefits, antihypertensive treatment
is not curative, must be life-long, and is very costly. In 1998,
$108 billion in health care spending was attributed to hypertension
in the US. The medical, economic, and human costs of untreated and
inadequately controlled high blood pressure are enormous
[15-34].
[0011] A previous method for evaluating and treating hypertension
has been proposed in U.S. Pat. No. 6,632,180 (2003) and U.S. Pat.
No. 6,595,926 to Laragh J. H. This method is manual, not based on
statistical inference, is not designed to work with ABPM, and does
not account for chronopharmatheucal effects. Other methods for
evaluating antihypertensive treatment based on ABPM have been
described in the scientific literature and are public domain
(described below).
[0012] As mentioned earlier, ABPM has drastically improved the
ability to assess the efficacy of antihypertensive treatment in
clinical studies and in medical practice [3-5]. Consequently,
state-of-the art diagnosis, treatment, and evaluation of
antihypertensive therapy is based on ABPM. Despite the significant
advantages of ABPM, the current indices and available techniques
for ABPM analysis are limited. For instance, duration and
homogeneity of antihypertensive drugs are commonly quantified by
computation of the TP and SI [7, 9-14]. Normally both the TP and
the SI are calculated from ABPM recordings obtained from individual
subjects and have important limitations when applied to populations
[11,35-38]. Evaluation of antihypertensive treatment in populations
is often carried out by calculating these individual indices for
each of the subjects and providing summarizing statistics about the
population such as the mean and median. However, the lack of a
well-defined population index (i.e. an index specifically developed
to analyze population data as opposed to individual ABPM
recordings) has resulted in methodological inconsistencies
regarding the description of antihypertensive drug effect at the
population level. Currently, researchers do not follow a
standardized methodology to conduct and report results on
populations. This limits significantly the comparability and
reproducibility of results involving the evaluation of
antihypertensive treatment, and prevents the use of evidence-based
medicine by practitioners. Additionally, given the limited
information provided by these indices to characterize
antihypertensive therapy, it is normally required to perform
additional statistical analysis of the ABPM recordings to
characterize the antihypertensive therapy. Leading experts in the
research community have pointed out the limitations of the TP
index. For instance, a leading researcher has stated "although it
is widely employed, this index has a lot of limitations" [12],
another leading scientist also pointed out that "the lack of a
specific methodology for estimating the TP initially led to
considerable confusion in the literature with each investigator
taking a unique approach to obtaining a TP value", warned that
"there are still important methodological issues that have yet to
be resolved", and recommended that "the use of the TP should be
reconsidered and probably abandoned" [35]. The SI index was
introduced to overcome some of the limitations of the TP index and
was shown to correlate with end-organ damage [39]. However, the SI
is also limited and leading researchers have concluded that
"overall, neither index has been proven to offer definitive
superiority" [11], and cautioned of the intrinsic limitations of
these techniques to evaluate and compare antihypertensive treatment
by stating that "any inference on the clinical superiority of one
particular treatment regime agent over another based on a higher
TP, MER or SI remains largely speculative in nature" [13].
[0013] Both the TP and SI have established definitions in the
literature for their evaluation on individual subjects. However,
most studies involving assessment of antihypertensive effects are
based on populations, and require researchers to report an index to
characterize the population or the specific antihypertensive
treatment under study. The typical approach to solve this problem
has been to evaluate the TP and SI for each individual subject in
the sample population under study, and to use summarizing
statistics such as the mean or median to report results to
characterize the population. Another approach has been to adapt
and/or redefine individual indices so that they can be calculated
directly from the population, leading to the concept of population
indices (i.e. indices calculated directly on the population) versus
individual indices (i.e. indices calculated on individual
subjects).
[0014] Before the introduction of the SI in 1998, the TP was the
only established index used for assessment of antihypertensive
treatment. Initially, the characterization of populations was done
by reporting the mean of the individual indices, that is, the mean
of the TPs [9, 40]. However, since the TP does not follow a normal
distribution Omboni proposed to characterize the population by
providing the median of the individual TPs [12,41,42]. In addition
to the median of the individual TPs, it was later proposed by
Meredith, Stergiou, and Mancia to provide also a measure of
dispersion such as the range of the individual TP values [11], the
inter-quartile range [14], or the 5th and 95th percentiles [43,44].
This methodology was not universally adopted by the research
community, and recent studies have used the mean to characterize
the population and in some cases the mean of responders [45,46].
Additionally, there is another methodology proposed by Stewart that
consists in calculating the so-called population TP, as the ratio
of the mean of all the individual troughs and the mean of all the
individual peaks [47, 48].
[0015] In the case of the SI, since its introduction it was
reported to follow a normal distribution
[0016] . As a consequence, it is most commonly reported on
populations by providing the mean of the individual SIs and the
standard error [12,14,39,43-46].
[0017] Consequently, the design and development of a well-designed
method to statistically characterize and compare antihypertensive
treatment in individuals and populations is an important problem
identified by the research community and practitioners.
SUMMARY
[0018] The present invention discussed herein provides a novel
method, system, and apparatus--the RDH Method--for evaluating
antihypertensive treatment efficacy across patient populations. In
accordance to one embodiment, the RDH is a population vector index
and graphical method that provides the means for the statistical
assessment of antihypertensive treatment reduction, duration, and
homogeneity using ambulatory blood pressure monitoring (ABPM). The
population RDH was specifically designed as a tool to evaluate and
compare blood pressure (BP) coverage offered by antihypertensive
drugs over 24 h in populations. In accordance to one embodiment,
the population RDH is a three-component vector index that
incorporates information about the reduction, duration, and
homogeneity of antihypertensive treatment, as well as their
statistical significance over the 24 h period. In the preferred
embodiment, the population RDH components quantify: 1) the total
number of statistical significant BP reductions, 2) the maximum
number of consecutive statistical significant reductions, and 3)
the maximum number of consecutive non-significant reductions over
the 24 hours, respectively; and reports two population graphs that
characterize the effect of the treatment. The output of the RDH
index can be used in clinical trials to characterize the effects of
antihypertensive medications, and in clinical practice to guide
antihypertensive treatment.
DRAWINGS/FIGURES
[0019] FIG. 1 shows an example of the graphical results detailing
the antihypertensive effect on the patient population according to
one embodiment of the said RDH method proposed (Analysis based on
SBP). Comparison of the RDHp on the treated versus non-treated
groups. (a) Nonparametric RDHp. (b) Parametric RDHp. (c)
Nonparametric RDHp . . . 20
[0020] FIG. 2 shows an example of the graphical results detailing
the antihypertensive effect on the patient population according to
one embodiment of the said RDH method proposed (Analysis based on
DBP). Comparison of the RDHp on the treated versus non-treated
groups. (a) Nonparametric RDHp. (b) Parametric RDHp. (c)
Nonparametric RDHp. Analysis based on DBP . . . 21
[0021] FIG. 3 shows an example of the graphical results detailing
the antihypertensive effect on the patient population and
individuals according to one embodiment of the said RDH method
proposed. Nonparametric RDH population plot for treated group
(analysis based on SBP). The top plot shows the individual RDH
sequence for each subject. In this plot a gray square indicates an
statistically significant reduction, the absence of a square
corresponds to a non-significant BP reduction, and a white square
denotes a time category where no data was available to perform the
statistical test. This graph complements the RDHp plot by
displaying the RDH corresponding to each individual subject in the
population under study. The bottom plot in this graph shows the
proportion of statistically significant reductions in each
category, and whether the population RDH resulted in a
statistically significant reduction (gray circle) or in a
non-significant reduction (white circle) . . . 22
[0022] FIG. 4 shows an example of the graphical results detailing
the antihypertensive effect on the patient population and
individuals according to one embodiment of the said RDH method
proposed. Nonparametric RDH population plot for non-treated group
(analysis based on SBP). The top plot shows the individual RDH
sequence for each subject. In this plot a gray square indicates an
statistically significant reduction, the absence of a square
corresponds to a non-significant BP reduction, and a white square
denotes a time category where no data was available to perform the
statistical test. This graph complements the RDHp plot by
displaying the RDH corresponding to each individual subject in the
population under study. The bottom plot in this graph shows the
proportion of statistically significant reductions in each
category, and whether the population RDH resulted in a
statistically significant reduction (gray circle) or in a
non-significant reduction (white circle). This visualization tools
enables researchers to quickly compare treatment or populations. As
expected, the number of statistical significant reductions is much
lower in the non-treated group than in the treated group . . .
23
DETAILED DESCRIPTION--PREFERRED EMBODIMENT
[0023] Given an individual ABPM recording, we denote each of the
time categories by an index k, where {k}.sub.k=1.sup.K. For the
purposes of describing this particular embodiment we will assume we
have 24 categories (K=24) corresponding to 24 h. Let L.sub.k
represent number of BP samples in the k-th class at baseline. In
general, the dimension of vectors from different classes is not
equal, that is, L.sub.k.noteq.L.sub.j where k and j denote the
index of the k-th and j-th class. Analogously, let L.sub.k.sup.1
number of BP samples in the k-th class after treatment. In general,
L.sub.k.noteq.L.sub.k.sup.1, that is, the dimension of the vector
before treatment corresponding to the k-th category is not
necessarily equal to the dimension of the vector after treatment
corresponding the same category. Let x denote vector containing the
individual BP values before treatment, and let x.sub.k,i denote the
i-th sample belonging to time category k,
x 1 = ( x 1 , 1 , x 1 , 2 , , x 1 , L 1 ) x 2 = ( x 2 , 1 , x 2 , 2
, , x 2 , L 2 ) x 24 = ( x 24 , 1 , x 24 , 2 , , x 24 , L 24 ) ( 1
) ##EQU00001##
The vector y containing the BP values after treatment for the same
subject is defined analogously,
y 1 = ( y 1 , 1 , y 1 , 2 , , y 1 , L 1 ' ) y 2 = ( y 2 , 1 , y 2 ,
2 , , y 2 , L 2 ' ) y 24 = ( y 24 , 1 , y 24 , 2 , , y 24 , L 24 '
) ( 2 ) ##EQU00002##
Let x.sub.k, y.sub.k denote the sample mean of the ABPM vector
corresponding to the k-th category before and after treatment,
x _ k = i = 1 L k x k , i L k , y _ k = i = 1 L k ' y k , i L k ' ,
##EQU00003##
and let x, y be vectors containing sample means before and after
treatment,
x=( x.sub.1, x.sub.2, . . . , x.sub.24)
y=( y.sub.1, y.sub.2, . . . , y.sub.24) (3)
The vector containing the class-by-class differences is denoted as
d,
d = x _ - y _ = ( x _ 1 , x _ 2 , , x _ 24 ) - ( y _ 1 , y _ 2 , ,
y _ 24 ) = ( d 1 , d 2 , , d 24 ) ( 4 ) ##EQU00004##
In order to define the population RDH we define x.sub.k.sup.j to be
x.sub.k for subject j. Given J subjects in the population under
study, we have
x 1 1 = ( x 1 , 1 1 , x 1 , 2 1 , , x 1 , L 1 , 1 1 ) x 24 1 = ( x
24 , 1 1 , x 24 , 2 1 , , x 24 , L 24 , 1 1 ) x 1 2 = ( x 1 , 1 2 ,
x 1 , 2 2 , , x 1 , L 1 , 2 2 ) x 24 2 = ( x 24 , 1 2 , x 24 , 2 2
, , x 24 , L 24 , 2 2 ) x 1 J = ( x 1 , 1 J , x 1 , 2 J , , x 1 , L
1 , J J ) x 24 J = ( x 24 , 1 J , x 24 , 2 J , , x 24 , L 24 , J J
) ( 5 ) ##EQU00005##
the vector y.sub.k.sup.j is defined analogously.
[0024] The population RDH can be calculated based on parametric or
nonparametric statistics. The advantage of the nonparametric RDH is
that it minimizes the number of assumptions made.
[0025] The parametric population RDH is obtained as follows: For
each category k, the population RDH takes as an input the set of
before {x.sub.k.sup.j}.sub.j=1.sup.J and post-treatment
{y.sub.k.sup.j}.sub.j=1.sup.J ABPM recordings, and generates a
three component vector index according to the following
algorithm:
[0026] Calculate the mean of each category k for each subject j
before and after the treatment
x _ k j = i = 1 L k , j x k , i j L k , j y _ k j = i = 1 L k , j '
y k , i j L k , j ' ( 6 ) ##EQU00006##
[0027] Create population composites of category k, before x.sub.k
and after treatment y.sub.k,
x k = ( x _ k 1 , x _ k 2 , , x _ k j , , x _ k J ) ( 7 ) y k = ( y
_ k 1 , y _ k 2 , , y _ k j , , y _ k J ) ( 8 ) ##EQU00007##
[0028] Create vector containing the BP differences,
d.sub.k=x.sub.k-y.sub.k=( x.sub.k.sup.1- y.sub.k.sup.1,
x.sub.k.sup.2- y.sub.k.sup.2, . . . , x.sub.k.sup.J-
y.sub.k.sup.J)=(d.sub.1, d.sub.2, . . . , d.sub.J) (9)
[0029] Perform a paired-sample t test to test if the mean BP
reduction in category k is greater than zero,
t k = d _ k se ^ d _ k = j = 1 J x _ k j - y _ k j J s d k 2 J s d
k 2 = j = 1 J ( d j - d _ ) 2 J - 1 ( 10 ) ##EQU00008##
that is, for each category k, k=1, . . . , 24, we assess the
statistical significance of of the mean BP reduction by dividing
the mean BP difference d.sub.k for category k over its standard
error s .sub. d.sub.k.
[0030] We define the population RDH vector as RDH=(c.sub.1,
c.sub.2, c.sub.3) where [0031] c.sub.1=Total number of
statistically significant reductions [0032] c.sub.2=Maximum number
of consecutive statistically significant reductions [0033]
c.sub.3=Maximum number of consecutive statistically non-significant
reductions
[0034] Since in general J>30, the t distribution approximates
the Normal distribution, and the threshold of 1.645 from the Normal
distribution can be used to establish statistical significance.
[0035] The nonparametric population RDH is based on bootstrap to
estimate the probability density function of the mean BP
differences for category k across the population and perform a
nonparametric test [49]. The nonparametric population RDH takes as
an input the set of before {x.sub.k.sup.j}.sub.j=1.sup.J and
{y.sub.k.sup.j}.sub.j=1.sup.J ABPM recordings and generates a three
component vector index according to the following algorithm
[0036] Create Vector vector containing the BP differences,
d.sub.k=x.sub.k-y.sub.k=( x.sub.k.sup.1- y.sub.k.sup.1,
x.sub.k.sup.2- y.sub.k.sup.2, . . . , x.sub.k.sup.J- y.sub.k.sup.J)
(11)
Note that even though the probability model of x.sub.k and y.sub.k
follows the two-sample model, the probability model for the
inter-population RDH follows a one-sample model,
T.sub.k.fwdarw.d.sub.k=(d.sub.k,1, d.sub.k,2, . . . ,
d.sub.k,J)
where as previously defined d.sub.k,j= x.sub.k.sup.j- y.sub.k.sup.j
and T.sub.k is the distribution function for category k.
[0037] Calculate the statistic of interest from d.sub.k,
{circumflex over (.theta.)}.sub.k=s(d.sub.k), which in this case is
the mean BP reduction d.
.theta. ^ k = s ( d k ) = j = 1 J d k , j J ( 12 ) ##EQU00009##
[0038] Use the empirical distribution {circumflex over (T)}.sub.k
to obtain bootstrap samples d.sub.k*=(d.sub.k,1*, d.sub.k,2*, . . .
, d.sub.k,J*) by random sampling of {circumflex over (T)}.sub.k
{circumflex over (T)}.sub.k.fwdarw.d.sub.k*=(d.sub.k,1*,d.sub.k,2*,
. . . ,d.sub.k,J*)
from which we can calculate bootstrap replications of the statistic
of interest {circumflex over (.theta.)}.sub.k=s(d.sub.k*) to
estimate the probability distribution {circumflex over
(.theta.)}.sub.k*.
[0039] Use the histogram of {circumflex over (.theta.)}.sub.k*(b),
b=1, 2, . . . , B as an estimate of the probability density
function of the mean BP differences for category k across the
population. The bootstrap confidence intervals for the population
BP reduction in class k are obtained as
{circumflex over (.theta.)}.sub.k.sub.lo=100.alpha..sup.th
percentile of {circumflex over (.theta.)}.sub.k*'s distribution
{circumflex over (.theta.)}.sub.k.sub.lo=100(1-.alpha.).sup.th
percentile of {circumflex over (.theta.)}.sub.k*'s distribution
(13)
[0040] If this interval contains zero, it cannot be assumed with
(1-2.alpha.) confidence that the parameters of the two populations
are statistically different.
[0041] Define the nonparametric population RDH vector as
RDH=(c.sub.1, c.sub.2, c.sub.3) analogous to the parametric
case.
Operation: The Following Description Exemplifies how to Interpret
the Results of the Preferred Embodiment of the Method or System
when used to Analyze Population ABPM Data in Order to Statistically
Evaluate an Antihypertensive Treatment and its Relationship to
Prior Art--Tp And Si--
[0042] FIG. 1 shows a comparison of a treated group versus a non
treated group based on the population RDH (RDHp) described in this
paper. In FIG. 1, the RDH index was computed from analysis of the
SBP population data. These figures show the results using the
parametric (FIG. ??-1(b)) and the nonparametric (FIG. 1(a)-1(c))
versions of the RDH index. Note that both tests lead to the same
results. In FIG. ??-1(b) the top plot shows the BP reductions
normalized in units of standard errors, the bottom plot shows the
statistical (grey) and nonstatistical (white) reductions. In FIG.
1(a)-1(c) the top shows the mean BP reduction and the Bootstrap
confidence intervals for each time category. In the case of the
treated group, RDHp=(24,24,0), which indicates that there were
statistically significant reductions in all the 24 time categories.
Based on this RDHp value we can conclude that treatment is a drug
with a 24-h duration of action. Furthermore, the RDHp plot shows
the estimated confidence intervals and the estimated mean BP
reduction. Based on the RDHp plot we can also state that the
treatment induced a mean BP reduction of 15 mmHg approximately. The
confidence intervals indicate that the reduction is homogeneous
across the 24-h period. On the other hand, we see that in the case
of the non-treated subjects, RHDp=(9,8,8), that is, there were 9
statistically significant reductions, 8 consecutive statistically
significant reductions, and 8 consecutive non-significant
reductions. Note that the graph of the RDH index clearly shows that
all the statistical significant reductions occurred between hour 3
and hour 10 after waking up. This result suggests that there is an
"ABPM Effect" in the first 10 hours of ABPM [50]. The RDHp plot
indicates that the mean reduction due to this ABPM effect is
approximately 3 mmHg.
[0043] Additionally, the RDHp can be used to test the effectiveness
of a given antihypertensive treatment on a specific population by
comparing the upper confidence interval against a threshold
different from zero. For instance, the RDHp can be used to test the
number of statistical significant and effective reductions by
comparing the confidence interval against a 5 mmHg threshold. Even
without performing the statistical test, the current nonparametric
RDHp graph showing the confidence intervals can be used for this
purpose. In FIG. 1(a), for instance, we can see that if the test
threshold were changed from 0 to -7 mmHg, all the reductions would
still be statistical significant. Thus, we can conclude that this
treatment not only induces statistical significant reductions
across the 24 h period, but also that this reductions are all
effective against a -7 mmHg threshold. Note that if we were to
apply the same criteria to the non-treated group (FIG. 1(c)), none
of the reductions would come out statistical significant,
indicating non-effectiveness.
[0044] FIG. 2 shows a comparison of the treated versus the
non-treated groups based on the RDHp computed from analysis of the
DBP population data. In the treated group, RDHp=(24,24,0), which
indicates that there were statistically significant reductions in
all the 24 time categories. Based on this RDHp value we can
conclude that treatment also induces an statistically significant
reduction on the DBP of 24-h duration. In the case of the non
treated group, RHDp=(8,6,8). From the RDHp graph we can see that
the mean BP reduction is lower in the DBP than SBP. This difference
is approximately 5 mmHg in the treated group (15 mmHg vs 10 mmHg
approximately).
[0045] FIG. 3 and FIG. 4 show a graphical representation of the
individual RDHs, and a comparison between the treated and the non
treated groups on SBP using the nonparametric RDH. The top plot
shows the individual RDH sequence for each subject. In this plot a
gray square indicates an statistically significant reduction, the
absence of a square corresponds to a non-significant BP reduction,
and a white square denotes a time category where no data was
available to perform the statistical test. This graph complements
the RDHp plot by displaying the RDH corresponding to each
individual subject in the population under study. The bottom plot
in this graph shows the proportion of statistically significant
reductions in each category, and whether the population RDH
resulted in a statistically significant reduction (gray circle) or
in a non-significant reduction (white circle). This graphical
representation enables researchers to immediately identify the
non-responder subjects (i.e. subjects for whom the antihypertensive
treatment did not induced statistically significant reductions
across the 24-h period).
* * * * *